Have you ever had to do math homework on the bus? Well it isn't the best place for it, but Kelsey is trying to do just that. Take a look.

On the morning after the trip to the museum, Kelsey realized that she had forgotten to do her math homework. She took out her math notebook on the bus. Everything was going fine until she saw this problem.

Kelsey isn't sure how to solve this problem, but she is sure that she can solve it in her head. Do you know?

This Concept will teach you how to use mental math to divide by decimal powers of ten. Then we'll come back to the homework.

Guidance

You have already learned how to multiply by what appears to be a power of ten after a decimal place. Remember that all powers of ten that you see written to the right of a decimal point are equal.

.10 = .100 = .1000 = .10000

When we multiply by this power of ten to the right a decimal point, we move the decimal point one place to the left.

When we divide by a power of ten to the right a decimal point, we are going to move the decimal point one place to the right.

If you think about this it makes perfect sense. The powers of ten written to the right of a decimal point are all equal. It doesn’t matter if you are multiplying or dividing by .10 or .100 or .1000. Division is the opposite of multiplication so you move the decimal point one place to the right.

Once you have learned the rule, you can use mental math to complete the division of decimals by a power of ten.

Example A

.67
.10
_____

Solution: 6.7

Example B

12.3
.100
_____

Solution: 123

Example C

4.567
.1000
_____

Solution: 45.67

Now back to the math homework. Here is the original problem once again.

On the morning after the trip to the museum, Kelsey realized that she had forgotten to do her math homework. She took out her math notebook on the bus. Everything was going fine until she saw this problem.

Kelsey isn't sure how to solve this problem, but she is sure that she can solve it in her head.